## Question

###### StatementSwimsuit development took massive leap forward in 2009 with the introduction of 'Speedo LZR' suits with polyurethane suits such as the 'Arena X-Glide' It was hypothesized that the suits reduced the effective cross sectional body area of the swimmer and the drag coefficient when moving through water; which would lead reduction in the drag force: The increase in performance may have been reduced by the fatiguing effect of the relatively stiff swimsuits, which would imp

Statement Swimsuit development took massive leap forward in 2009 with the introduction of 'Speedo LZR' suits with polyurethane suits such as the 'Arena X-Glide' It was hypothesized that the suits reduced the effective cross sectional body area of the swimmer and the drag coefficient when moving through water; which would lead reduction in the drag force: The increase in performance may have been reduced by the fatiguing effect of the relatively stiff swimsuits, which would impact more in the longer events with large number of turns_ To test this hypothesis suppose YOu suggest the mathematica model for the velocity U of the swimmer propelling in the /-direction through water as Ilb(p,c)II = ()", where P is the metabolic power exerted by the swimmer t0 propel her body; â‚¬ is the drag coefficient; and k and are empirica constants such that k,n 2 0. The reasoning for this model is that the swimmer can increase her swimming speed by increasing her exerted metabolic power or reducing the drag coefficient wearing the X-Glide suit; or by combination of both: You want to test how effective each of these_ Tasks Find an expression for bivariate function f(x,y) Y in terms of_ and â‚¬ . where and are the fractional change in speed resulting from change in metabolic power and the drag coefticient respectively. What are the mathematica and physical limitations on the rate of expenditure of metabolic energy with time? Calculate the gradient of f (x,Y) in terms of _ and â‚¬ Find and plot the equation of the tangent plane to the surface 2 = f (x,y) and the parametric equations of the normal line at the point To [+j + k for a suitable value of parameter Suppose that the power exerted by the swimmer is directly proportional to her body mass index (B) which in turn depends on the swimmers height (h) and mass (m) as B(m,h) = The mass and height would change with the swimmer's age (A) If A is the constant of proportionality relating power to the body mass index draw tree diagram and find an expression for the rate of change speed with age terms Of x,m,h, and